Question: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{14}{3} \left(\dfrac{3}{2}\right)^{i - 1}$ What is $a_{3}$, the third term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{14}{3}$ and the common ratio is $\dfrac{3}{2}$ To find $a_{3}$ , we can simply substitute $i = 3$ into the given formula. Therefore, the third term is equal to $a_{3} = -\dfrac{14}{3} \left(\dfrac{3}{2}\right)^{3 - 1} = -\dfrac{21}{2}$.